The background to this query was this question.
I have installed this driver for Firebird and placed it within the path (system32) used by the IDE. The XE Data Explorer
The first thing that sticks out to me is that you're using the 64-bit version of Firebird, and that you mentioned it comes with both a 32- and 64-bit driver. Are the DLLs named the same? If so, I suspect that the IDE/OS are trying to load the 64-bit version of the DLL in a 32-bit application, which isn't possible (32-bit apps can't load 64-bit drivers, and vice versa).
Try one of two things:
First, if the DLLs have the same name, rename the 64-bit version temporarily, and restart the IDE. Then try again.
Try installing the 32-bit version of Firebird, even though you're running a 64-bit OS.